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Question 34727: Exact Value of a Numerical Ratio

On this page
  1. Original question and givens
  2. Definition and scope
  3. Step-by-step derivation
  4. Reverse checks
  5. Result
  6. This question review and source binding

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R0068-34727 · q-20260930-r02-ratio-exact-value-0002

Original question and givens

In the rational numerical-ratio setting, find the exact value of -11:(-2). The consequent is nonzero; answer as a reduced p/q with a positive denominator.

  • G001 — In the rational numerical-ratio setting, find the exact value of -11:(-2). The consequent is nonzero; answer as a reduced p/q with a positive denominator.

Definition and scope

Use the original question domain, assumptions and cited MKO definitions. This item has second-context mathematical and bilingual review, with the model, answer and every arithmetic step independently recomputed from the original parameters; the source question remains a candidate.

Step-by-step derivation

S001 · implies

Before

source roles = [qf-ratio-exact-value, [a, b, operation]]

After

derived = [ratio_value, no-invented-domain]

Conditions: none

Separate source banks:legacy RAW SAFE with unbounded derived BigInts versus BASE Number.isInteger without invented SAFE/million caps.Operations,domains and permissive/exact keys follow THIS bank.Keep ORIGINAL JSON intact.

Step identifiers and dependencies

Rule: R68_BANK_specific_keys_operations_and_numeric_guards · Uses: G001

S002 · calculation

Before

Ratio ORIGINAL antecedent divided by NONzero consequent := div(-11, -2)

After

Ratio ORIGINAL antecedent divided by NONzero consequent = 11/2

Conditions: none

Calculate exactly from ORIGINAL ordered operands;mul/sub/div have EXPLICITLY TWO operands.Legacy derived BigInts are not recapped at RAW SAFE;check BASE Number type/representation conditions separately.Do not use floating approximations to force an answer.

Step identifiers and dependencies

Rule: exact_rational_arithmetic · Uses: G001, S001

S003 · implies

Before

source roles = [-11, -2]

After

derived = [11/2]

Conditions: none

The ORDERED numerical ratio a:b is a/b,FIRST requiring b≠0.Negative inputs are allowed;reduce by gcd and make the denominator positive,RETAINING/1 for integers.Do not invert the ratio or infer arbitrary dimensional division.

Step identifiers and dependencies

Rule: Ratio_ORDERED_numerical_ratio_reduced_positive_denominator · Uses: G001, S002

Reverse checks

  • S003 · premise_and_result_audit — Reverse-check THIS question’s ORIGINAL givens,domain and step premises.Preserve originals/English/MKOs/ASTs/status;do not reverse a one-way implication or call finite checks independent review or general formal proof.
  • S002 · premise_and_result_audit — Recompute Ratio ORIGINAL antecedent divided by NONzero consequent with exact rational arithmetic, not rounded decimals.
  • S001 · premise_and_result_audit — Reverse-check THIS question’s ORIGINAL givens,domain and step premises.Preserve originals/English/MKOs/ASTs/status;do not reverse a one-way implication or call finite checks independent review or general formal proof.

Result

11/2

The full substitutions and premise checks give the original answer; source identity,format and status are unchanged.

This question review and source binding

Review date: 2026-10-26

Original questions, answers, step expressions, numeric ASTs and historical records are retained. Source candidate labels remain historical and are not overwritten as formal proof.

Source hashes and review receipts
  • input commit: 0f7be61e2c22317a4075561dc822c87d881a50db
  • original question SHA-256: 61e84b0cdeb0f960d838dd2090e302dec6c6796a4f84984a1fefae421288c9fc
  • candidate record SHA-256: 3ab146b85ee1d0e2a48d091ddff7c6ec79c3e77891991e871aebef8b7ffcc090
  • semantic review receipt SHA-256: e7a54104fa02c235f7591329bd6db8d626dd74bf0fae29c557b1f269c85066ed
  • question-first witness SHA-256: 8401a3c2064c1275a6a7ea8f00412fa12286cec7b2db6c305ff9dba3724ae229
  • Lean: NOT_RUN · human review: NOT_PERFORMED
Same-source full JSON